wrong results in test_commonmatrix

[1e9abhi1e10]

from https://github.com/sympy/sympy/blob/master/sympy/matrices/tests/test_commonmatrix.py#L354

m = Matrix(3, 3, [1, x**2 + 2*x + 1, y, (x + 1)**2, 2, 0, y, 0, 3])
assert m.is_symmetric() # True
assert not m.is_symmetric(simplify=False) #False 
assert m.expand().is_symmetric(simplify=False) #True 

But

>>> m
Matrix([
[         1, x**2 + 2*x + 1, y],
[(x + 1)**2,              2, 0],
[         y,              0, 3]])

>>> m.transpose()
Matrix([
[             1, (x + 1)**2, y],
[x**2 + 2*x + 1,          2, 0],
[             y,          0, 3]])

m[1,2] = x**2 + 2*x + 1 and m[2,1] = (x + 1)**2 which are not equal, therefore m is not symmetric and the method would return False.
But current behavior on master isTrue
see also #24671

[ThePauliPrinciple]

Surely they are equal in the mathematical meaning?

>>> ((x+1)**2).expand()
x**2 + 2*x + 1

[ThePauliPrinciple]

https://docs.sympy.org/latest/tutorials/intro-tutorial/gotchas.html#equals-signs

You can read about it here, which uses exactly the example we are discussing here.

[1e9abhi1e10]

Should I compare the results of sage math and sympy, sorry if not.
In sage math I got False for this :

sage: m = Matrix(3, 3, [1, x**2 + 2*x + 1, y, (x + 1)**2, 2, 0, y, 0, 3])
sage: m.is_symmetric()
False

[ThePauliPrinciple]

I don't know about sage math. But can you please write explicitly whether you agree that in mathematics the following equality holds: x**2 + 2*x + 1 = (x+1)**2 = (x+1)*(x+1)= x**2 + x*1 + 1*x + 1**2?

[1e9abhi1e10]

I totally agree with your statement but if we think in this way then what is the use of expand and simplify

[ThePauliPrinciple]

m.is_symmetric(simplify=True) is the default in SymPy

sympy/sympy/matrices/common.py

Lines 1748 to 1754 in c4d6b3e

	def is_symmetric(self, simplify=True):
	"""Check if matrix is symmetric matrix,
	that is square matrix and is equal to its transpose.
	By default, simplifications occur before testing symmetry.
	They can be skipped using 'simplify=False'; while speeding things a bit,
	this may however induce false negatives.

So it checks if it is "mathematically" symmetric if you use m.is_symmetric(). Which is what master does for me and what the test is testing for.

If you want to test for "structural" symmetry, you have to set it to False (maybe that is the default for sage?)

expand will be applied to all elements of a Matrix, so both off diagonals will (in this case) expand to the same expression

[sylee957]

I consider simplify argument for is_symmetric design flaw because it can be replaced with M.applyfunc(simplify).is_symmetric(simplify=False)

[1e9abhi1e10]

Are these tests look good for you?

m = Matrix(3, 3, [1, x**2 + 2*x + 1, y, (x + 1)**2, 2, 0, y, 0, 3])
assert m.is_symmetric() # True
assert not m.is_symmetric(simplify=False) #False 
assert m.expand().is_symmetric(simplify=False) #True